Question

∠dca and ∠dcb are right angles. what else is needed to prove △adc≅△bdc by the hl congruence theorem? da≅db only da≅db and ac≅bc angle a≅angle b ac≅bc only

Explanation:

Step1: Recall HL congruence theorem

HL (Hypotenuse - Leg) congruence theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.
In right - triangles \(\triangle ADC\) and \(\triangle BDC\), \(DC\) is the common leg (\(DC\cong DC\) by reflexive property).

Step2: Identify hypotenuse

For \(\triangle ADC\) and \(\triangle BDC\) to be congruent by HL, we need the hypotenuses to be congruent. The hypotenuses of \(\triangle ADC\) and \(\triangle BDC\) are \(DA\) and \(DB\) respectively.

Answer:

DA≅DB only